The German tactician has generally enjoyed positive results at the club’s home ground, but Atalanta easily defeated the Reds on Wednesday
Never before in Klopp’s previous 137 competitive matches in charge at Liverpool’s home ground had the club lost by more than one goal.
The last time the Reds suffered such a heavy defeat at Anfield dates back to August 2015, when Brendan Rodgers saw his side lose 3-0 to West Ham in the Premier League.
On Wednesday, Liverpool simply struggled to get going against their Serie A opponents and failed to register a single shot on target – the first time they’ve done so in the Champions League since Opta began recording such data in 2003.
Goal 50 Revealed: The best 50 players in the world
Atalanta, meanwhile, continued their recent good form in the competition and struck twice in the space of five minutes via Josip Illcic and Robin Gosens.
Klopp did field an experimental starting side at Anfield with teenage trio Curtis Jones, Rhys Williams and Neco Williams all included from the off.
“We didn’t get going. We know it was a poor performance and that we were pretty flat,” Milner told BT Sport.
“A lot of players have not played together and the schedule is busy. Sometimes you have to try and get a win without being your best but we didn’t have that sharpness.
“We are still top of the group so have to recover and go again at the weekend. The effort is always there. They took their chances at the right time. The whole game we were maybe a second late on the press and created very few chances.
“It was one of those nights where we didn’t produce our best. We need to move on from it pretty quickly because we have a lot of games coming up. It’s in our hands and we have to look where we can improve.”
Despite the defeat, the Reds remain top of Group D but are only two points ahead of Ajax and Atalanta.